12 and 13 please ◀️⬆️⬇️↗️↩️⬅️↖️↔️

A bullet with a mass ????b=13.5mb=13.5 g is fired into a block of wood at velocity ????b=253vb=253 m/s. The block is attached to

Lorico [155]

Answer:

450 grams

Explanation:

Given:

mass of the bullet, m = 13.5 g = 0.0135 kg

velocity of the bullet, v = 253 m/s

spring constant of the spring, k = 205 N/m

Compression of the spring, x = 35.0 cm = 0.35 m

Now, the kinetic energy of the moving system (bullet + board) will tend to move the spring

thus,

let velocity of the system, V

now, applying the concept of conservation of momentum, we have

mv = (M + m)V

where,

M is the mass of the block

thus,

V = mv/(M + m)

now,

the kinetic energy of the system = (1/2)(M + m)V²

or

the kinetic energy of the system = (1/2)(M + m)(mv/(m + M))²

Energy gained by the spring = (1/2)kx²

now,

equating both the energies, we get

(1/2)(M + m)(mv/(m + M))² = (1/2)kx²

or

(mv)²/(m + M) = kx²

on substituting the values, we get

(0.0135 × 253)²/(0.0135 + M) = 205 × (0.35)²

or

11.66/(0.0135 + M) = 25.1125

or

M = 0.450 kg = 450 grams

8 0

4 years ago

A 45.2-kg person is on a barrel ride at an amusement park. She stands on a platform with her back to the barrel wall. The 3.74-m

elena-14-01-66 [18.8K]

Answer:

1,230N

Explanation:

1. Name of the variables:

$f:frequency\\\\ \omega:angular\text{ }speed\\\\ a_c:centripetal\text{ }acceleration\\\\ F_c:centripetal\text{ }force\\ \\ m:mass\\ \\ d:diameter\\ \\ r:radius\\ \\ g:gravitational\text{ }acceleration$

2. Formulae:

$f=\dfrac{number\text{ }of\text{ }revolutions}{time}$

$\omega=2\pi f$

$a_c=\omega^2 r$

$F_c=m\times a_c$

3. Solution (calculations)

$f=\dfrac{1}{1.65s}=0.\overline{60}s^{-1}$

$\omega=2\pi\times0.\overline{60}\approx 3.808rad/s$

$a_c=(3.808rad/s)^2\times (3.74/2m)=27.12m/s^2$

$F_c=45.2kg\times27.12m/s^2=1,225.67N\approx 1,230N$

3 0

3 years ago

Calculate (a) the torque, (b) the energy, and (c) the average power required to accelerate Earth in 4.0 days from rest to its pr

natima [27]

<h2>Answer:</h2>

Torque = 2.05 x 10²⁸ Nm

Energy = 3.54 x 10³³ J

Average power = 1.02 x 10²⁸ W

<h2>Explanation:</h2>

(a) Torque (τ) is the rotational effect of a given force.

It is given by

τ = I x α -------------(i)

Where;

I = rotational inertia of the object

α = angular acceleration of the object.

In this case, the object is the Earth. Therefore,

I = 9.71 x 10³⁷ kg m²

α = ω / t

Where;

ω = angular velocity of earth = 2π rad / day

Since 

1 day = 24 hours and 1 hour = 3600seconds

1 day = 24 x 3600 seconds = 86400seconds

=> ω = 2π rad / 86400seconds

=> ω = 7.29 × 10⁻⁵ rad/s

t = 4 days = 4 x 24 x 3600 seconds = 345600 seconds

=> α = ω / t

=> α = 7.29 × 10⁻⁵ / 345600

=> α = (7.29 × 10⁻⁵) / (3.456 x 10⁵)

=> α = (7.29 × 10⁻⁵⁻⁵) / (3.456)

=> α = (7.29 × 10⁻¹⁰) / (3.456)

=> α = 2.11 × 10⁻¹⁰ rad/s²

Now substitute the values of I and α into equation (i)

τ = 9.71 x 10³⁷ x 2.11 × 10⁻¹⁰

τ = 9.71 x 10²⁷ x 2.11

τ = 20.5 x 10²⁷ Nm

τ = 2.05 x 10²⁸ Nm

(ii) The energy (rotational energy) E is given by;

E = $\frac{1}{2}$ x I x ω

E = $\frac{1}{2}$ x 9.71 x 10³⁷ x 7.29 × 10⁻⁵

E = 35.4 x 10³² J

E = 3.54 x 10³³ J

(iii) The average power P, is given by;

P = E / t

P = 3.54 x 10³³ / 345600

P = 1.02 x 10²⁸ W

5 0

3 years ago

A thin walled spherical shell is rolling on a surface. What

ExtremeBDS [4]

Answer:

$=\frac{1/3}{5/6} = 0.4$

Explanation:

Moment of inertia of given shell $= \frac{2}{3} MR^2$

where

M represent sphere mass

R -sphere radius

we know linear speed is given as $v = r\omega$

translational $K.E = \frac{1}{2} mv^2 = \frac{1}{2} m(r\omega)^2$

rotational $K.E = \frac{1}{2} I \omega^2 = \frac{1}{2} \frac{2}{3} MR^2 \omega^2$

total kinetic energy will be

$K.E = \frac{1}{2} m(r\omega)^2 + \frac{1}{2} \frac{2}{3} MR^2 \omega^2$

$K.E =\frac{5}{6} MR^2 \omega^2$

fraction of rotaional to total K.E

$=\frac{1/3}{5/6} = 0.4$

8 0

3 years ago

Q. At what point in a waterfall do the drops of water contain the most kinetic energy ?

antoniya [11.8K]

Answer:

2.When they reach the bottom of the fall

Explanation:

The potential energy of the waterfall is maximum at the maximum height and decreases with decrease in height. Based on the law of conservation of mechanical energy, as the potential energy of the water fall is decreasing with decrease in height of the fall, its kinetic energy will be increasing and the kinetic energy will be maximum at zero height (bottom of the fall).

Thus, the correct option is "2" When they reach the bottom of the fall

7 0

3 years ago